Hint: If two process are independent then P(A = a, B = b) = P(A = a) * P(B = b) and P(A|B) = P(A = a,B = b)/P(B=b)
Assume that when the German plays Hungary in soccer, each team scores independently as a homogeneous Poisson process with rates λGermany = 1 and λHungary = 3 goals per game.
a) Expected number of total goals in a single game.
b) Expected number of total goals scored in the first half, given that 2 total goals were scored in the entire game.
c) Expected number of goals Germany scored in the entire game, given that 2 total goals were scored in the first half.
What I really need help with is getting the formulas for parts b & c. I'm having difficulty forming what the Expectation formula should be. `
Thanks for the help,
at this point I'm still having trouble with part c of this problem.
I've come to the conclusion that if I use the conditional expectation of
E(X|X + Y = n) = (λ1 / λ1 + λ2) * n
I might get to the answer, however I'm not sure how to account for the fact that our given statement states two goals were scored in the first half